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Diophantine equation

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A Diophantine equation is an multi-variable equation for which integer solutions (or sometimes natural number or whole number solutions) are to be found.

Finding the solution or solutions to a Diophantine equation is closely tied to modular arithmetic and number theory. Often, when a Diophantine equation has infinitely many solutions, parametric form is used to express the relation between the variables of the equation.

Diophantine equations are named for the ancient Greek/Alexandrian mathematician Diophantus.

A Diophantine equation in the form is known as a linear combination. If two relatively prime integers and are written in this form with , the equation will have an infinite number of solutions. More generally, there will always be an... [more]